Question

you are dealt one card from a 52 - card deck. find the probability that you are dealt a club or a non - picture card. click the icon to view a description of a standard deck of playing cards. the probability is (type an integer or a simplified fraction.)

Explanation:

Step1: Calculate the number of club cards and non - picture cards

• A standard deck has 52 cards.
• There are 13 club cards.
• There are 40 non - picture cards (since there are 12 picture cards in a deck: 4 Jacks, 4 Queens, 4 Kings). But we have double - counted the non - picture club cards. The non - picture club cards are 10 (Ace through 10 in clubs).
• Using the formula \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\), where \(A\) is the set of club cards and \(B\) is the set of non - picture cards. So \(n(A) = 13\), \(n(B)=40\), \(n(A\cap B)=10\). Then \(n(A\cup B)=13 + 40-10=43\).

Step2: Calculate the probability

• The probability \(P\) of an event is given by \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes is \(n(A\cup B) = 43\) and the total number of outcomes is 52. So \(P=\frac{43}{52}\).

Answer:

\(\frac{43}{52}\)